Usually people put a bounding volume of some kind around each object or mesh, such as an axis-aligned bounding box (AABB) or a sphere. These simplified shapes can easily and quickly be checked against the frustum (you can search for AABB-versus-frustum or sphere-versus-frustum intersection tests). The object is drawn if its bounding volume intersects the frustum, which is a conservative estimate of what's visible.
For more efficient frustum culling of large numbers of objects, a hierarchy of bounding volumes is used, such as an AABB tree, sphere tree, octree or BSP tree.
Note that if you're just trying to get the camera working, you should avoid frustum culling and simply draw all objects each frame, then put the frustum culling in later once you've got other things working (since it is a bit of a fiddly process with the potential for lots of odd bugs).